1. Field of the Invention
The present invention relates to an adaptive equalization method applicable to a data transmission system which transmits a send signal, composed of plural pieces of data, from a transmitting to a receiving device over a transmission line. More particularly, the invention pertains to an adaptive equalization method which is used when the receiving device reconstructs or reproduces a pseudo send signal by removing signal distortion components (intersymbol interference) contained in the received signal due to various noise components and reflected waves,
2. Description of the Prior Art
FIG. 15 is a block diagram illustrating the configuration of a data transmission system employing a conventional adaptive equalization method. In FIG. 15, reference numeral 1 denotes a transmitting device, 2 a modulator placed in the transmitting device 1 to generate and output a send signal composed of plural pieces of transmission data, 4 a receiving device, 3 a transmission line for transmitting the send signal to the receiving device 4, 5' an adaptive equalizer placed in the receiving device 4 to estimate the send signal from the received signal sent over the transmission line 3 and output it as the above-mentioned pseudo send signal, and 6 a demodulator for demodulating the pseudo send signal to coding information.
The operation of the conventional data transmission system will be described below.
To begin with, in the transmitting device 1 the modulator 2 generates a send signal composed of plural pieces of data, from predetermined coding information, and outputs it. The send signal is transmitted over the transmission line 3 to and received by the receiving device 4. In the receiving device 4, the adaptive equalizer 5' reconstructs a pseudo send signal by removing various noise components and signal distortion components (intersymbol interference) contained in the received signal due to reflected waves or the like and then the demodulator 6 demodulates the pseudo send signal to obtain coding information.
in such a data transmission system, if the pseudo send signal output from the adaptive equalizer 5' corresponds exactly with the actual send signal output from the modulator 2, then the receiving device 4 can derive, from the pseudo send signal, coding information that matches the predetermined coding information of the transmitting device 2. On the other hand, if the pseudo send signal differs from the actual send signal, then the receiving device 4 will have erroneous coding information.
As described above, the adaptive equalizer 5' is used to reconstruct the send signal from the received signal, and hence it plays an important role in determining the likelihood of data in the data transmission system. The adaptive equalizer 5' will be described below in detail.
FIG. 16 illustrates in block form an example of the conventional adaptive equalizer 5'. Respective pieces of data of the received signal are sequentially input into the adaptive equalizer 5', which responds thereto to output respective pieces of data of the pseudo send signal one after another. In FIG. 16, reference numeral 211, . . . , 21N denote data holding means for holding plural pieces of received data input thereinto in the past; 220, . . . , 22N denote plural tap coefficient multiplying means which are each provided corresponding to one of the plural pieces of previously received data and newly received data, for multiplying the corresponding received data by a predetermined tap coefficient and outputting the multiplied data; 231, . . . , 23N denote adding means for adding together the plural pieces of multiplied data and outputting the added data; 24 and 25 denote error output means for outputting error data contained in the added data on the basis of decided values of the received data; 26 and 27 denote step size multiplying means for multiplying the error data by a step size and outputting a step value; 280, . . . , 28N denote instantaneous gradient calculating multipliers each for multiplying the corresponding step value and received data and outputting an instantaneous gradient value; and 360, ... , 36N and 350, . . . , 35N denote tap coefficient output means each for calculating, based on the corresponding instantaneous gradient value, a tap coefficient for use at the next received data input timing. The added data is output as pseudo send data based on the received data.
Such a configuration is commonly called an FIR (Finite impulse Response) filter. The adaptive equalizer has a circuit configuration based on the LMS (Least Mean Square) algorithm.
The tap coefficient thus obtained matches a tap coefficient obtainable with the following equation (3). EQU C(n+1)=C(n)+.mu..multidot..gradient.(n) (3)
where C(n+1) is a tap coefficient by which (n+1)th received data is multiplied, C(n) a tap coefficient by which (n)th received data is multiplied, .mu. a step size, and .gradient.(n) a gradient vector based on the (n)th received data. In the LMS algorithm, the instantaneous gradient vector is calculated by the following equation (4). EQU .gradient.(n)=e(n).multidot.x(n) (4)
where e(n) is an error contained in (n)th pseudo transmission data and x(n) is (n)th received data.
Because of such a configuration as mentioned above, the conventional adaptive equalizer has a problem that the mean square of errors contained in the pseudo transmission data is far larger than a mean square error contained in a Wiener solution that is considered to minimize it. And, an excess error that is obtained by subtracting the mean square error in the Wiener solution from the mean square error in the LMS algorithm constitutes a major factor in limiting the maximum likelihood of the pseudo send data in the LMS algorithm, degrading the equalization performance of the adaptive equalizer that utilizes the LMS algorithm.
incidentally, the Weiner solution needs to be calculated using the steepest descent method or the like, but arithmetic processing by the steepest descent method is required to use a gradient vector that is obtained by an expected value calculation; hence, the calculation of the Weiner solution involves the expected value calculation by a matrix such as an auto-correlation matrix or cross-correlation vector. In the actual calculation of the Weiner solution, it is necessary to use plural pieces of received data while at the same time repeating the expected value calculation by the matrix through the use of each received data, besides the number of received data for use in the expected value calculation steadily increases and the computational complexity of the expected value calculation increases at a geometric rate accordingly. Therefore, a circuit or program adapted to calculate the Weiner solution by the steepest descent method needs to perform very complex arithmetic processing of enormous amounts of data, and hence it has not been put to practical use. For reference purposes, an operation expression for the gradient vector by the Weiner solution is shown by the following equation (5). EQU .gradient.(n)=E[e(n).multidot.x[n]] (5)
where x[n] is a vector composed of plural pieces of received data that are input into the equalizer, e(n) is an error contained in the pseudo transmission data and E[.multidot.] means the expected value calculation.
For the reasons given above, it is impossible at present to implement adaptive equalization processing through utilization of the steepest descent method, and the adaptive equalization processing is now performed using the LMS algorithm easier to implement than the steepest descent method.
Next, a brief description will be given of the mean square error that arises excessively in the LMS algorithm. As will be seen from a comparison of Eqs. (2) and (3), the LMS algorithm can be considered as an algorithm for calculating the gradient vector by using the instantaneous value calculation as a substitute for the expected value calculation in the steepest descent method. Accordingly, letting the mean square error remaining in the Weiner solution be represented by {character pullout}min, the excessively remaining mean square error {character pullout}ex(LMS) (excess error) in the LMS algorithm can be given by the following equation (6): EQU {character pullout}ex(LMS)=.mu..multidot.trace[R].multidot.{character pullout}min (6)
where R is an auto-correlation matrix of received data and trace[R] is the sum of eigen values of the auto-correlation matrix.